Phase-shift interferometry is an established method for measuring a variety of physical parameters ranging from intrinsic properties of gases to the displacement of objects such as described in a review article by J. Schwider entitled “Advanced Evaluation Techniques In Interferometry,” Progress In Optics XXVII, Ed. E. Wolf (Elsevier Science Publishers 1990). The contents of the Schwider article are herein incorporated in their entirety by reference. Interferometric wavefront sensors can employ phase-shift interferometers (PSI) to measure the spatial distribution of a relative phase across an area or two-dimensional section, i.e., to measure a physical parameter across a two-dimensional section.
An interferometric wavefront sensor employing a PSI typically consists of a spatially coherent light source that is split into two beams, a reference beam and a measurement beam, which are later recombined after traveling respective optical paths of different lengths. The relative phase difference between the wavefronts of the two beams is manifested in a two-dimensional intensity pattern or interference signal known as an interferogram. PSIs typically have an element in the path of the reference beam which introduces three or more known phase-shifts. By detecting the intensity pattern with a detector for each of the phase-shifts, the relative phase difference distribution of the reference and measurement beam wavefronts can be quantitatively determined independent of any attenuation in either of the reference or measurement beams.
Phase shifting in homodyne detection methods using phase shifting methods such as piezo-electric driven mirrors have been widely used to obtain high-quality measurements under otherwise static conditions. The measurement of transient or high-speed events have required in prior art either ultra high speed phase shifting, i.e., much faster than the event time scales and corresponding detector read out speeds, or phase shifting apparatus and methods that can be used to acquire the required information by essentially instantaneous measurements.
Several methods of spatial phase shifting have been disclosed in the prior art. In 1983 Smythe and Moore described a spatial phase-shifting method in which a series of conventional beam-splitters and polarization optics are used to produce three or four phase-shifted images onto as many cameras for simultaneous detection. A number of US patents such as U.S. Pat. No. 4,575,248, U.S. Pat. No. 5,589,938, U.S. Pat. No. 5,663,793, U.S. Pat. No. 5,777,741, and U.S. Pat. No. 5,883,717 disclose variations of the Smythe and Moore method where multiple cameras are used to detect multiple interferograms. One of the disadvantages of these methods is that multiple cameras are required or a single camera recording multiple images and complicated optical arrangements are required to produce the phase-shifted images. The disadvantages of using multiple cameras or a camera recording multiple images are described for example in the commonly owned U.S. patent application Ser. No. 10/765,368 (ZI-47) entitled “Apparatus and Method for Joint Measurements of Conjugated Quadratures of Fields of Reflected/Scattered and Transmitted Beams by an Object in Interferometry” by Henry A. Hill. The contents of U.S. patent application Ser. No. 10/765,368 are herein incorporated in their entirety by reference.
An alternative technique for the generation of four simultaneous phase-shifted images for a homodyne detection method has also been disclosed by J. E. Millerd and N. J. Brock in U.S. Pat. No. 6,304,330 B1 entitled “Methods And Apparatus For Splitting, Imaging, And Measuring Wavefronts In Interferometry.” The technique disclosed in U.S. Pat. No. 6,304,330 B1 uses holographic techniques for the splitting of a beam into four beams. The four beams are detected by a single pixelated detector. One consequence of the use of a single pixelated detector to record four phase-shifted images simultaneously is a reduction in frame rate for the detector by a factor of approximately four compared to a PSI recording a single phase-shifted image on a single pixelated detector with the same image resolution. It is further observed that since the generation of the multiple beams in the technique described in U.S. Pat. No. 6,304,303 B1 is performed on a non-mixed beam of an interferometer, the alternative technique of U.S. Pat. No. 6,304,303 B1 is most readily applicable to for example a Twyman-Green type interferometer.
Another alternative technique for generating the equivalent of multiple simultaneous phase shifted images has also been accomplished by using a tilted reference wave to induce a spatial carrier frequency to a pattern in an interferogram, an example of which is disclosed by H. Steinbichler and J. Gutjahr in U.S. Pat. No. 5,155,363 entitled “Method For Direct Phase Measurement Of Radiation, Particularly Light Radiation, And Apparatus For Performing The Method.” This another alternative technique for generating the equivalent of multiple simultaneous phase shifted images requires the relative phase of the reference and measurement field to vary slowly with respect to the detector pixel spacing.
The another alternative technique for generating the equivalent of multiple simultaneous phase shifted images using a tilted reference wave is also used in an acquisition technology product FlashPhase™ of Zygo Corporation. The steps performed in FlashPhase™ are first acquire a single frame of intensity or interferogram, next generate a two-dimensional complex spatial frequency map by a two-dimensional finite Fourier transform (FFT), next generate a filter and use the filter to isolate a first order signal, then invert the filtered spatial frequency map by an inverse two-dimensional FFT to a phase map or wavefront map. Although the acquisition technology product FlashPhase™ is computationally complex, it is very fast on today's powerful computers.
Other methods of generating simultaneous multiple phase-shifted images include the use of gratings to introduce a relative phase shift between the incident and diffracted beams, an example of which is disclosed in U.S. Pat. No. 4,624,569. However, one of the disadvantages of these grating methods is that careful adjustment of the position of the grating is required to control the phase shift between the beams.
Yet another method for measuring the relative phase between two beams is disclosed in U.S. Pat. No. 5,392,116 in which a linear grating and five detector elements are used. However, this method only measures the difference in height of two adjacent spots on a measurement object and not the simultaneous measurement of a two-dimensional array of spots on the measurement object. The method also generates a set of multiple beams as a mixed beam of an interferometer and therefore has a similar limitation to the technique described in U.S. Pat. No. 6,304,303 B1 wherein the alternative technique of U.S. Pat. No. 6,304,303 B1 is most readily applicable to for example a Twyman-Green type interferometer.
A disadvantage of the techniques for generating simultaneous multiple phase shifted images described in U.S. Pat. No. 6,304,303 B1 is a first order sensitivity to variations in the relative sensitivities of conjugate sets of detector pixels and to variations in corresponding properties of the optical system used to generate the four phase shifted images wherein a conjugate set of pixels is four.
It is noted that wavefront sensing can be accomplished by non-interferometric means, such as with Hartmann-Shack sensors which measure the spatially dependent angle of propagation across a wavefront. These types of sensors are disadvantageous in that they typically have much less sensitivity and spatial resolution than interferometric wavefront sensors.
Variable frequency and multiple frequency sources have been used to measure and monitor the relative path length difference such as described in U.S. Pat. No. 5,412,474 entitled “System For Measuring Distance Between Two Points Using A Variable Frequency Coherent Source” by R. D. Reasenberg, D. Phillips, and M. C. Noecker and in references contained therein. The contents of U.S. Pat. No. 5,412,474 are herein incorporated in their entirety by reference. The variable frequency source techniques have further been used to remove phase redundancy in making absolute distance measurements.
Prior art also teaches the practice of interferometric metrology using heterodyne techniques and a detector having a single detector element or having a relatively small number of detector elements. Prior art further teaches the practice of interferometric metrology using a step and stare method with a single-homodyne detection method for the acquisition of conjugated quadratures of fields of reflected and/or scattered beams when a detector is used that comprises a large number of detector elements. The term single-homodyne method is used hereinafter for homodyne detection methods wherein the reference and measurement beams each comprise one component corresponding to a component of a conjugated quadratures. The respective conjugated quadrature of a field is |a|sin φ when the quadrature x(φ) of the field is expressed as |a|cos φ.
The step and stare method and single-homodyne detection method are used in prior art in order to obtain for each detector element a set of at least three electrical interference signal values with a substrate that is stationary with respect to the respective interferometric metrology system during the stare portion of the step and stare method. The set of at least three electrical interference signal values are required to obtain for each detector element conjugated quadratures of fields of a measurement beam comprising a reflected and/or scattered field from a spot in or on a substrate that is conjugate to the each detector element.
Commonly owned prior art teaches the practice of acquisition of the respective at least three electrical interference signal values in interferometric metrology when operating in a relatively fast scanning mode wherein each of the at least three electrical interference signal values corresponds to the same respective spot on or in a substrate and contain information that can be used for determination of joint measurements of conjugated quadratures of fields in both spatial and temporal coordinates.
As will be appreciated from the description presented below, various embodiments of the invention described herein involve scanning and non-scanning interferometric metrology using a single- and multiple-homodyne detection methods to obtain non-joint and joint measurements, respectively, of conjugated quadratures of fields either reflected and/or scattered or transmitted by a substrate with a detector having a large number of detector elements, that exhibits an intrinsic reduced sensitivity to effects of vibrations and environmental changes, and that enables compensation of effects of vibrations and of environmental changes. The classification of multiple-homodyne detection methods is used hereinafter for homodyne detection methods wherein the reference and measurement beams each contain information about two components of each of one or more conjugated quadratures. For each spot in and/or on the substrate that is imaged a corresponding set of at least three electrical interference signal values is obtained. Each of the set of at least three electrical interference signal values contains information for determination of either a non-joint or a joint measurement of respective conjugated quadratures of fields and in addition contains information for the enablement of a procedure for the compensation of effects of vibrations and of environmental changes in the phases corresponding to conjugated quadratures as cyclic errors.
Prior art teaches a homodyne detection method, referenced herein as a double homodyne detection method, that is based on use of four detectors wherein each detector generates an electrical interference signal value used to furnish information about a corresponding component of a conjugated quadratures of a field such as described in cited U.S. Pat. No. 6,304,303 B1 and in Section IV of the article by G. M D'ariano and M G. A. Paris entitled “Lower Bounds On Phase Sensitivity In Ideal And Feasible Measurements,” Phys. Rev. A 49, pp 3022-3036 (1994). The four detectors generate the four electrical interference signal values simultaneously and each electrical interference signal value contains information relevant to one conjugated quadratures component. Accordingly, the double homodyne detection method does not make joint determinations of conjugated quadratures of fields wherein each electrical interference value contains information simultaneously about each of two orthogonal components of the conjugated quadratures although the four electrical interference signal values are obtained jointly with respect to time.
Various multiple-homodyne detection methods described herein, e.g., the bi-homodyne and quad-homodyne detection methods, obtain measurements of the at least three electrical interference signal values wherein each measured value of an electrical interference signal contains simultaneously information about two orthogonal components of a conjugated quadratures. The faster rate for the determination of conjugated quadratures is achieved when using the quad-homodyne detection method relative to the bi-homodyne detection method to obtain the measured values of the electrical interference signal values in two measurements. The next fastest rate for the determination of conjugated quadratures is obtained when operating the bi-homodyne detection method configured for operation with a set of three phase shift values.
Compensation for effects of vibrations and environmental changes as described herein is implemented by two different procedures. In each of the two different procedures, advantage is taken of properties of various embodiments of the invention with respect to compensation for effects of vibrations and environmental changes as cyclic errors. In one procedure, the compensation for the effects of vibrations and environmental changes is based on information obtained when operating in the reference frame to reduce the effects of vibrations and environmental changes.
In the reference frame, the optical path length difference between a spot on the reference object and a corresponding spot on the measurement object is maintained a constant value mod 2π at the reference frequency. The reference frequency is controlled by using information from a portion of the reference and measurement beams or a portion of the information contained in the respective two-dimensional arrays of electrical interference signal values corresponding to the corresponding spots on the reference and measurement objects.
A description of the first procedure is given in the corresponding portion of the description of the first embodiment of the present invention. In the second procedure, a spatial frequency is introduced into the relative path length between the reference and measurement beam objects and the effect of the spatial frequency is used in the measurement of the cyclic errors in the phases of measured conjugated quadratures that represent the effects of vibration and environmental changes. The measured values of cyclic errors are used in a subsequent procedure to compensate for the effects of vibrations and environmental changes. The measured values of cyclic errors may also be used to monitor changes in position, angular orientation, and/or deformation of a measurement object corresponding to phase measurements mod 2π. The monitored changes in position, angular orientation, and/or deformation corresponding to phase measurements mod 2π can be used as an error signal to a servo systems that control either the reference frequency and/or the relative positions, angular orientations, and/or deformations of the reference and measurement objects corresponding to phase measurements mod 2π.
The error signal used to monitor changes in the relative position of the corresponding portions of the reference and measurement objects comprises two-dimensional spatial Fourier components of the phases of the conjugated quadratures of relative path length differences between the reference and measurement objects corresponding to the cyclic errors. The information about changes in the relative angular orientation of the reference and measurement objects is obtained by using linear displacement information about two different portions of the array of relative path length differences between the reference and measurement objects. The information about changes in relative deformations of the reference and measurement objects is obtained by using linear displacement information about three or more different portions of the array of relative path length differences between the reference and measurement objects.
The spatial frequency is introduced into the relative path length between the reference and measurement beam objects by introducing a tilt between the reference and measurement objects. The role of the tilt which may be used is different from the roles of the tilt used in the product FlashPhase™ and in published US Patent Application 20050046864 entitled “Simultaneous phase-shifting Fizeau interferometer” by J. E. Millerd and J. C. Wyant. In US Patent Application 20050046864, the tilt is used to make it possible to separate the reference and measurement beams after the reference and measurement objects, respectively, so that the reference and measurement beams can be optically processed separately before subsequently recombining the optically processed reference and measurement beams to form mixed output beams. In FlashPhase™, the tilt is used to introduce a spatial carrier frequency that enables the extraction of conjugated quadratures across a wavefront from a single array of measured electrical interference signal values. The tilt in both cases is not used to generate information about the effect of the vibrations and environmental changes.
In the second procedure described herein, the tilt is used to generate information about the effects of the vibrations and environmental changes that appear as cyclic errors for subsequent use in compensation for the effects of the vibrations and environmental changes including the effects of rotation and deformations.
With respect to information content and signal-to-noise ratios, the conjugated quadratures of fields obtained jointly in an interferometric metrology system that is operating in a scanning mode and using either the bi-homodyne or quad-homodyne detection methods are substantially equivalent to conjugated quadratures of fields obtained when operating the interferometric metrology system in a step and stare mode, i.e., a non-scanning mode. The conjugated quadratures of fields obtained jointly when operating in the scanning mode and using either the bi-homodyne or the quad-homodyne detection methods also have reduced sensitivity, i.e., only in second and higher order effects, to pinhole-to-pinhole variations in properties of a conjugate set of pinholes used in a confocal microscopy system and reduced sensitivity, i.e., only in second and higher order effects, to pixel-to-pixel variation of properties within a set of conjugate pixels of a multipixel detector in confocal and non-confocal microscopy systems.
The conjugated quadratures of fields obtained jointly when operating in the scanning mode and using either the bi-homodyne or the quad-homodyne detection method further have reduced sensitivity, i.e., only in second and higher order effects, to pulse to pulse variations of the input beam used in generating the conjugated quadratures of fields and can exhibit reduced sensitivity, i.e., only in second and higher order effects, to a relative motion of a substrate being imaged during the acquisition of joint measurements of the conjugated quadratures of fields. The reduced sensitivity is relative to conjugated quadratures of fields obtained when operating with a single-homodyne detection method in either a scanning or non-scanning mode. In microscopy applications, conjugated quadratures of fields are obtained for each spot in and/or on a substrate that is imaged.
The conjugated quadratures of fields that are obtained jointly in a non-dispersion and dispersion linear or angular displacement interferometer operating in a scanning mode and using either the bi-homodyne or the quad-homodyne detection methods have a reduced phase redundancy problem as compared to non-dispersion and dispersion linear or angular displacement interferometer operating in a scanning mode and using a single-homodyne detection method.
The signal-to-noise ratios obtained operating in the reference frame are generally greater than the signal-to-noise ratios obtained when not operating in the reference frame such as with the techniques for generating simultaneous multiple phase shifted images in the presence of vibrations and environmental changes.